| In this dissertation, the empirical likelihood method proposed by Owen (1988) is applied to achieve the following goals: First, based on the method of empirical likelihood, the estimation of the population mean with a known coefficient of variation is studied and compared with some well-known estimators in the nonparametric setting. Simulation studies show that the estimator based on the empirical likelihood technique performs better than some well-known estimators. Tests of hypotheses based on the empirical likelihood ratio are also discussed.; Second, we consider testing statistical hypotheses involving inequalities on the basis of the method of empirical likelihood. We also consider estimating M-functionals in the presence of auxiliary information given by inequalities. The empirical likelihood method makes it possible to use the auxiliary information more efficiently in the estimation problem.; Third, we discuss a density estimation problem under a two-sample semi-parametric model which arises under a case-control sampling plan. In particular, we propose a data-driven procedure for bandwidth selection. We compare the proposed procedure with some commonly used methods via a numerical study.; Finally, we use the empirical likelihood method to test for changes from a distribution to a weighted distribution. The non-parametric and semi-parametric change-point models encompass many important families of distributions such as the exponential family and the “partially exponential” family. The non- and semi-parametric maximum likelihood estimates of change-points are constructed and are shown to be consistent. The test statistics and confidence intervals are given based on the empirical likelihood ratios. We present some bootstrap procedures to find critical values for the proposed test. We also propose a method to test the validity of our change-point models. These methods are applied to some real data sets such as Nile River data and the British Coal Mine data. All the results match those in the literature. |
